Question

In figure ⬆

ABCD is a parallelogram, AE perpendicular to DC and CF perpendicular to AD. If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD


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Answer 1

Step-by-step explanation:

In parallelogram ABCD, we have given AB=10cm, AE=8cm, and CF=12cm.

⇒ AB=DC=10cm [Opposite sides of parallelogram are equal]

⇒ Lets find out area of parallelogram with height AE and base DC.

⇒ Area of parallelogram ABCD=b×h

⇒ Area of parallelogram ABCD=DC×AE

⇒ 10×8

∴ Area of parallelogram ABCD=80cm

2

--- ( 1 )

⇒ Now, to find area of parallelogram let CF be the height and AD will be base.

⇒ Area of parallelogram ABCD=CF×AD

⇒ 80=12×AD [From ( 1 )]

⇒ AD=

12

80

∴ AD=6.66cm

Answer 2

Answer:-

BSOWe have,

• AE ⊥ DC and AB = 16 cm

∵ AB = CD [Opposite sides of parallelogram]

• ∴ CD = 16 cm

Now, area of parallelogram ABCD = CD x AE

= (16 x 8) cm2 = 128 cm2 [∵ AE = 8 cm]

Since, CF ⊥ AD

∴ Area of parallelogram ABCD = AD x CF

• ⇒ AD x CF = 128 cm
• ⇒ AD x 10 cm = 128 cm2 [∵ CF= 10 cm]
• ⇒ AD =$\frac{128}{10}$

= 12.8 cm

Thus, the required length of AD is 12.8 cm

hope it helps u...!!